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Advances in Nano Research Volume 16, Number 5, May 2024 , pages 473-487 DOI: https://doi.org/10.12989/anr.2024.16.5.473 |
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Assessment of nonlocal nonlinear free vibration of bi-directional functionally-graded Timoshenko nanobeams |
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Elnaz Zare, Daria K. Voronkova, Omid Faraji, Hamidreza Aghajanirefah, Hamid Malek Nia, Mohammad Gholami and Mojtaba Gorji Azandariani
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| Abstract | ||
| The current study employs the nonlocal Timoshenko beam (NTB) theory and von-Kármán's geometric nonlinearity to develop a non-classic beam model for evaluating the nonlinear free vibration of bi-directional functionally-graded (BFG) nanobeams. In order to avoid the stretching-bending coupling in the equations of motion, the problem is formulated based on the physical middle surface. The governing equations of motion and the relevant boundary conditions have been determined using Hamilton's principle, followed by discretization using the differential quadrature method (DQM). To determine the frequencies of nonlinear vibrations in the BFG nanobeams, a direct iterative algorithm is used for solving the discretized underlying equations. The model verification is conducted by making a comparison between the obtained results and benchmark results reported in prior studies. In the present work, the effects of amplitude ratio, nanobeam length, material distribution, nonlocality, and boundary conditions are examined on the nonlinear frequency of BFG nanobeams through a parametric study. As a main result, it is observed that the nonlinear vibration frequencies are greater than the linear vibration frequencies for the same amplitude of the nonlinear oscillator. The study finds that the difference between the dimensionless linear frequency and the nonlinear frequency is smaller for CC nanobeams compared to SS nanobeams, particularly within the | ||
| Key Words | ||
| bi-directional functionally-graded; differential quadrature method; Eringen's nonlocal theory; nanobeams; nonlinear vibration | ||
| Address | ||
| Elnaz Zare and Mohammad Gholami:Department of Civil Engineering, Yasouj University, Yasouj, Iran Daria K. Voronkova: Department of Mathematics and Natural Sciences, Gulf University for Science and Technology, Mishref Campus, Kuwait/ Bauman Moscow State Technical University Moscow, Russia Omid Faraji: Department of Civil Engineering, Imam Hossein University, Tehran, Iran Hamidreza Aghajanirefah: Department of Civil Engineering, Faculty of Engineering, Qazvin Branch Islamic Azad University, Qazvin,Iran Hamid Malek Nia: Department of of Civil Engineering, Arak Branch, Islamic Azad University, Arak, Iran Mojtaba Gorji Azandariani: Department of Civil Engineering, Semnan University, Semnan, Iran/ Centre for Infrastructure Engineering, Western Sydney University, Sydney, Australia | ||